Problem: Simplify the following expression: $k = \dfrac{50t - 30s}{40s + 50} - \dfrac{50r + 10}{40s + 50}$ You can assume $r,s,t \neq 0$.
Solution: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{50t - 30s - (50r + 10)}{40s + 50}$ $k = \dfrac{50t - 30s - 50r - 10}{40s + 50}$ The numerator and denominator have a common factor of $10$, so we can simplify $k = \dfrac{5t - 3s - 5r - 1}{4s + 5}$